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Your firm spends $6,500 annually for electricity. Johnson Controls offers to install a new computer-controlled lighting system...

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Finance

Your firm spends $6,500 annually for electricity. JohnsonControls offers to install a new computer-controlled lightingsystem that will reduce electric bills by $1,000 in each of thenext 5 years. The system costs $1,450 to install and $2,750 todispose of at the end of 5 years. Assume the cost savings are knownwith certainty and the interest rate is 10%. What are the IRRs ofthe project? There should be two IRRs even if one of them is notuseful.

Answer & Explanation Solved by verified expert
3.8 Ratings (346 Votes)

We have found out the NPV under 3 scenarios:

Discount rate = 10% Discount rate = 44.765% Discount rate = -23.792%
Year CF Discount Factor DCF Discount Factor DCF Discount Factor DCF
0 -1450 1/1.10^0= 1 -1450*1= -1450 1/(1+0.447654405752536)^0= 1 -1450*1= -1450 1/(1+-0.2379237)^0= 1 -1450*1= -1450
1 1000 1/1.10^1= 0.909090909 1000*0.909090909090909= 909.0909091 1/(1+0.447654405752536)^1= 0.690772602 1000*0.690772601545166= 690.7726015 1/(1+-0.2379237)^1= 1.312204565 1000*1.31220456534339= 1312.204565
2 1000 1/1.10^2= 0.826446281 1000*0.826446280991735= 826.446281 1/(1+0.447654405752536)^2= 0.477166787 1000*0.477166787045476= 477.166787 1/(1+-0.2379237)^2= 1.721880821 1000*1.72188082130804= 1721.880821
3 1000 1/1.10^3= 0.751314801 1000*0.751314800901578= 751.3148009 1/(1+0.447654405752536)^3= 0.329613743 1000*0.329613742858351= 329.6137429 1/(1+-0.2379237)^3= 2.259459875 1000*2.25945987469764= 2259.459875
4 1000 1/1.10^4= 0.683013455 1000*0.683013455365071= 683.0134554 1/(1+0.447654405752536)^4= 0.227688143 1000*0.227688142659303= 227.6881427 1/(1+-0.2379237)^4= 2.964873563 1000*2.96487356278845= 2964.873563
5 -1750 1/1.10^5= 0.620921323 -1750*0.620921323059155= -1086.612315 1/(1+0.447654405752536)^5= 0.157280731 -1750*0.157280730645753= -275.2412786 1/(1+-0.2379237)^5= 3.890520625 -1750*3.89052062475693= -6808.411093
NPV = Sum of all DCF 633.253131 NPV = Sum of all DCF 0 NPV = Sum of all DCF 0
  • If the discount rate is 10% then the NPV is positive
  • If it is 44.765% then NPV = 0
  • If it is -23.792% then NPV = 0
  • As CFs have multiple sign changes there are multiple IRRs. But -23.792% is not relevant as it is a negative number
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Transcribed Image Text

Your firm spends $6,500 annually for electricity. JohnsonControls offers to install a new computer-controlled lightingsystem that will reduce electric bills by $1,000 in each of thenext 5 years. The system costs $1,450 to install and $2,750 todispose of at the end of 5 years. Assume the cost savings are knownwith certainty and the interest rate is 10%. What are the IRRs ofthe project? There should be two IRRs even if one of them is notuseful.

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